Dynamic harmonic balance and its application to analysis of convergence of second-order sliding mode control algorithms

The harmonic balance (HB) principle is extended to transient processes and named the dynamic HB. Based on the dynamic HB, first the differential equations for the amplitude and frequency of the self-excited oscillations in the Lure system in the vicinity of the periodic solution are derived. It is then applied to analysis of motions in the vicinity of the origin of the complex plane for systems with second-order sliding mode control algorithms, therefore, describing the process of convergence of state variables in the system. An example is provided.